Question

if -2 is a zero of a polynomial P(X) =ax³-x²+x+4 ,then find the value of "a"

Answer 1

Given ---
p(x) = ax³ - x² + x + 4
-2 is a zero of polynomial i.e. it leaves remainder 0
=> p(-2) = 0

To Find ---
the value of a

Finding ---

p(x) = ax³ - x² + x + 4
=> p(-2) = a × (-2)³ - (-2)² + (-2) + 4
= (a × -8) - (4) + (-2) + 4
= -8a - 4 - 2 + 4
= -8a - 2

But p(-2) = 0

=> 0 = -8a - 2
=> 8a = -2
=> a = -2/8
=> a = -1/4

Hence, a = -1/4
That's your answer.

Hope it'll help... :-D